Firstly I'd like to say- congratulations to you both on getting this far through and doing as well as you have.
Now- I have been through this exact situation, near enough- my Father was diagnosed with Prostate Cancer when I was about 6 months from doing my GCSEs -However there is some difference as he was a single parent.
For my part, I can say that the best thing he was do was process the news himself, then come to me once he'd considered things. Throughout, I was glad that I was told and trusted to be adult enough to "deal" with it. Did this affect me through my study and exams? Yes. Did he go into remission? Yes. Did it come back again, when I was studying and also doing my A-Levels? Yes.
However for all of this, being obejective, I know for sure I'd have been devestated for it to have gone otherwise- kids do take things on the chin and get used to certain bumps in the road and treat it as "just how things are"- but it's a sign of trust, responsibility and adulthood that they be informed, after all, you're family.
At the end of the day you're all there for one another, through thick and thin. It will only worry you and your wife more to continue dreading telling them, of knowing that you haven't told them and how it will affect them. Sure, they'll need support through this and the thought of that may seem be overwhelming considering the stress that your wife and you are going through, but equally your kids are there for you as well.
My Father took great solace in knowing that I knew, we were there for each other, we understood that some changes would need to be made here and there- that he didn't always have the energy to do things so I could help out and over time it meant I needed to be home more as well. But do I regret it? No. It gave me comfort to know I was there for him as well, just as your kids will take comfort for the same- otherwise they may feel they missed out on chances to do things that otherwise they'd never have done.
For one? Spend as much time as you can with them, another is taking photos, videos, immortalising memories and for both "sides" of the Cancer monster, from those with it and those supporting, to feel that they are and will be getting what they feel they need. It isn't just support and comfort, it's an appreciation and realization for life and what it means that you don't often have drop on your doorstep and for better or worse, it broadens your perspective.